Rate Profiles

Fig. 2.1. Rate profiles for nitration in 80-100% sulphuric acid. For references see table 3.3.

Fig. 3.3. Rate profiles for nitration at 25 °C corrected for variation in activity coefficients. ...

That the rate profiles are close to parallel shows that the variations in rates reflect the changing concentration of nitronium ions, rather than idiosyncrasies in the behaviour of the activity coefficients of the aromatic compounds. The acidity-dependences of the activity coefficients of / -nitrotoluene, o- and -chloronitrobenzene (fig. 2.2, 2.3.2), are fairly shallow in concentrations up to about 75 %, and seem to be parallel. In more concentrated solutions the coefficients change more rapidly and it... 

Generally the determination of the reactivity of a particular compound depends upon comparison of its rate of nitration with that of benzene at the same acidity and temperature. Because of the spread of rates this may not be practically possible and, in any case, is usually not necessary because of the parallelism existing among rate profiles (fig. 2.4). Reactivities in aqueous sulphuric acid are, in fact, very nearly independent of acidity, and stepwise comparison of data for a compound with those of benzene determined at different acidities is possible. 

There are certain limitations to the usefulness of nitration in aqueous sulphuric acid. Because of the behaviour of the rate profile for benzene, comparisons should strictly be made below 68% sulphuric acid ( 2.5 fig. 2.5) rates relative to benzene vary in the range 68-80% sulphuric acid, and at the higher end of this range are not entirely measures of relative reactivity. For deactivated compounds this limitation is not very important, but for activated compounds it is linked with a fundamental limit to the significance of the concept of aromatic reactivity as already discussed ( 2.5), nitration in sulphuric acid cannot differentiate amongst compounds not less than about 38 times more reactive than benzene. At this point differentiation disappears because reactions occur at the encounter rate. 

For deactivated compounds this limitation does not exist, and nitration in sulphuric acid is an excellent method for comparing the reactivities of such compounds. For these, however, there remains the practical difficulty of following slow reactions and the possibility that with such reactions secondary processes might become important. With deactivated compounds, comparisons of reactivities can be made using nitration in concentrated sulphuric acid such comparisons are not accurate because of the behaviour of rate profiles at high acidities ( 2.3.2 figs. 2.1, 2.3). 

Further problems arise if measurements of the rate of nitration have been made at temperatures other than 25 °C under these circumstances two procedures are feasible. The first is discussed in 8.2.2 below. In the second the rate profile for the compound imder investigation is corrected to 25 °C by use of the Arrhenius parameters, and then further corrected for protonation to give the calculated value of logio/i fb. at 25 °C, and thus the calculated rate profile for the free base at 25 °C. The obvious disadvantage is the inaccuracy which arises from the Arrhenius extrapolation, and the fact that, as mentioned above, it is not always known which acidity functions are appropriate. 

This method is exemplified by its application to quinoline, isoquinoline, cinnoline, and isoquinoline 2-oxide, which are nitrated as their conjugate acids. The rate profiles for these compounds and their N- or O-methyl perchlorates show closely parallel dependences upon acidity (fig. 2.4). Quaternisation had in each case only a small effect upon the rate, making the criterion a very reliable one. It has the additional advantage of being applicable at any temperature for which kinetic measurements can be made (table 8.1, sections B and D). 

Similar difficulties arise in the nitrations of 2-chloro-4-nitroaniline and /)-nitroaniline. Consideration of the rate profiles and orientation of nitration ( 8.2.5) these compounds suggests that nitration involves the free bases. However, the concentrations of the latter are so small as to imply that if they are involved reaction between the amines and the nitronium ion must occur upon encounter that being so, the observed activation energies appear to be too high. The activation energy for the simple nitration of the free base in the case of/>-nitroaniline was calculated from the following equation ... 

I The rate constants given refer to the acidities quoted, but the accompanying isomer proportions usually refer to slightly different acidities. However, as noted, isomer proportions are not much affected by changes in acidity. Rate profiles are available for all of the compounds. ... 

For this series of compounds qualitative information is quite extensive. Application of the criteria discussed in 8.2, in particular comparison with the corresponding methyl quaternary salt, establishment of the rate profile for nitration in sulphuric acid, and consideration of the encounter rate and activation parameters, shows that 2,4,6-collidine is nitrated as its cation. The same is true for the 3-nitration of 2,4- ... 

The similarity of their rate profiles, and the similarity of their rate constants for nitration at a particular temperature and acidity show that 4-pyridone, i-methyl-4-pyridone, and 4-methoxypyridine are all nitrated as their cations down to about 85 % sulphuric acid. The same is true of 2-methoxy-3-methylpyridine. In contrast, 3- and 5-methyl-2-pyridone, i,5-dimethyl-2-pyridone and 3-nitro-4-pyridone all react... 

The interest attaching to the nitration of pyridine i-oxide and its derivatives has already been mentioned ( 8.2.5). Some data for these reactions are given in tables 8.1, 8.2 and 8.4. The 4-nitration of pyridine I-oxide is shown to occur through the free base by comparison with the case of i-methoxypyridinium cation ( 8.2.2), by the nature of the rate profile ( 8.2.1), and by consideration of the encounter rate ( 8.2.3). - Some of these criteria have been used to show that the same is true for... 

TABLE in-45. RATE PROFILE SLOPES FOR NITRATION OF THIAZOLE (242)... 

Fig. 8. Drying time and rate profiles for leather pasted on glass plates and dried in two temperature stages. Gas velocity = 5 m/s in parallel flow, 71°C in the first stage, 57°C in the second. The falling rate, drying rate is proportional to residual moisture content.

The Ideal Fiber-Reactive Dye Profile. Eigure 3 shows the general profile for the apphcation of a reactive dye. In addition to showing the rate profile of fixation between dye and fiber, three other practical parameters (A—C) are noted. 

Temperature reaction rate profiles for representatives compounds are available (21,26). Particularly important are the operating temperatures required before destmction is initiated. Chemical reactivity by compound class from high to low is (27) alcohols > cellsolves/dioxane... 

In the section dealing with electrophilic attack at carbon some results on indazole homocyclic reactivity were presented nitration at position 5 (Section 4.04.2.1.4(ii)), sulfon-ation at position 7 (Section 4.04.2.1.4(iii)) and bromination at positions 5 and 7 (Section 4.04.2.1.4(v)). The orientation depends on the nature (cationic, neutral or anionic) of the indazole. Protonation, for instance, deactivates the heterocycle and directs the attack towards the fused benzene ring. A careful study of the nitration of indazoles at positions 2, 3, 5 or 7 has been published by Habraken (7UOC3084) who described the synthesis of several dinitroindazoles (5,7 5,6 3,5 3,6 3,4 3,7). The kinetics of the nitration of indazole to form the 5-nitro derivative have been determined (72JCS(P2)632). The rate profile at acidities below 90% sulfuric acid shows that the reaction involves the conjugate acid of indazole. 

According to a kinetic study which included (56), (56a) and some oxaziridines derived from aliphatic aldehydes, hydrolysis follows exactly first order kinetics in 4M HCIO4. Proton catalysis was observed, and there is a linear correlation with Hammett s Ho function. Since only protonated molecules are hydrolyzed, basicities of oxaziridines ranging from pii A = +0.13 to -1.81 were found from the acidity rate profile. Hydrolysis rates were 1.49X 10 min for (56) and 43.4x 10 min for (56a) (7UCS(B)778). O-Protonation is assumed to occur, followed by polar C—O bond cleavage. The question of the place of protonation is independent of the predominant IV-protonation observed spectroscopically under equilibrium conditions all protonated species are thermodynamically equivalent. 

A temperature profile plus a vapor-rate profile through the column must be assumed to start the procedure. These variables are referred to as tear variables and must be iterated on until convergence is achieved in which their values no longer change from iteration to iteration and all equations are satisfied to an acceptable degree of tolerance. Each iteration down and then up through the column is referred to as a column iteration. A set of assumed values of the tear variables consistent with the specifications, plus the component K values at the assumed temperatures, is as follows, using assumed end and middle temperatures and K values from Fig. 13-14. ... 

Equation (13-50) is used to calculate, from the previous stage, the (f/d) ratio on each stage in the rectifying section. The assumed temperature and phase-rate-profile assumptions conveniently fix all the A values for ideal solutions. The calculations are started by writing the equation for stage N ... 

Tbe values all are fixed by assumed temperature and pbase-rate profiles. Equation (13-55) is applied to eacb of tbe stripping stages in sequence until tbe ratio in tbe liquid entering tbe feed stage is obtained. 

The new temperature and flow-rate profiles (which would be used as the assumptions to begin the second column iteration) are compared in Fig. 13-46 with the final solution. Both profiles are moving toward the final result. 

TABLE 13-13 New Temperature and Rate Profiles from the First Trial of Example 3... 

Fig. 8.6. pH-Rate profile for release of salicylic acid fiom benz-aldehyde disalicyl acetal. [Reproduced firom E. Anderson and T. H. Fife, J. Am. Chem. Soc. 95 6437 (1973) by permission of the American Chemical Society.]... 

The pH-rate profile (see Fig. 8.6) indicates that of the species that are available, the monoanion of the acetal is the most reactive. The reaction is fastest in the intermediate pH range, where the concentration of this species is at a maximum. The concentration of the neutral molecule decreases with increasing pH the converse is true of the concentration of the dianion. 

The change in mechanism with pH for compound 1 gives rise to the pH-rate profile shown in Fig. 8.7. The rates at the extremities pH < 2 and pH > 9 are proportional to [H+] and [ OH], respectively, and represent the specific proton-catalyzed and hydroxide-catalyzed mechanisms. In the absence of the intramolecular catalytic mechanisms, the... 

Fig. 8.7. pH-Rate profile for compound 1. (Reproduced from Ref. 72 by permission of the American Chemical Society.)... 

Consider the alkaline pH region of the pH-rate profile in Fig. 8.4 (p. 459), which indicates a rate independent of pH. The rate-controlling reaction in this region is... 

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